- Vertical integral heating value = 8.90333 for all cases
#5-b.
m1: 466.667 km
m2: 233.333 km
#5-c.
#5-d.
#5-d. Discussion: Explain the nonlinear curve of KE with S.
Kinetic Energy (KE) is calculated as KE=(V^2)/2, and it depends on heating profile (q) because V is generated by heating.
Therefore, q and q^2 profiles are compared each other below at S=-0.5, -0.3, -0.1, and 0 (shallow convection cases).
As we can see, even though cumulated q(solid line) is same (=8.90333) all the cases, cumulated q^2(red solid line) is increased as absolute(S) increases.
This increasing is related to increased amplitude of mode 2 of heating as absolute(S) increases.
Therefore, KE has minimum value when S=0, and maximum when S=-0.5 and 0.5.
#5-e.
#5-e. Discussion: Implications for tropical cyclogenesis, in terms of convective heating profiles and their dependence on low-level rain evaporation and downdrafts.
T is calculated as below.
h = h0*exp(-x/Lr)
PHI(=geopotential) = gh = gz
p = (rho)RT & p = (rho)gz --> RT=gz = gh
This is Temperature profile at S=0.5 (stratiform case).
As we can see, mode 1 and mode 2 has opposite sign of temperature in lower levels.
In lower levels, mode 2(=stratiform mode) causes cold temperature and downdraft by evaporating cooling as it rains,
while mode 1(=convective mode) still causes updraft. Therefore, anticyclone by mode 2 and cyclone by mode 1 will be cancelled out, so cyclone will be weakened. This is unfavorable condition for cyclogenesis.
The opposite case is S=0.5 (shallow convection case) below.
In this case, mode 2(=shallow convection mode) will help to enhance cyclogenesis at lower levels.
+ about h0:
All calculations are performed without specified h0 in h=h0*exp(-x/Lr). (h0 is supposed to be 1 here.)
Therefore, all values are not realistic. If h0 is given, they would get more realistic values.
#5-a.
- Vertical integral heating value = 8.90333 for all cases#5-b.
m1: 466.667 kmm2: 233.333 km
#5-c.
#5-d.
#5-d. Discussion: Explain the nonlinear curve of KE with S.
Kinetic Energy (KE) is calculated as KE=(V^2)/2, and it depends on heating profile (q) because V is generated by heating.Therefore, q and q^2 profiles are compared each other below at S=-0.5, -0.3, -0.1, and 0 (shallow convection cases).
mode 1 = sin(m1z)
mode 2 = -S*sin(m2z)
q = mode 1 + mode 2
q^2 = q*q
As we can see, even though cumulated q(solid line) is same (=8.90333) all the cases, cumulated q^2(red solid line) is increased as absolute(S) increases.
cumulated q^2 = 8.75 (S=-0.5), 7.63 (S=-0.3), 7.07 (S=-0.1), and 7.0 (S=0).
This increasing is related to increased amplitude of mode 2 of heating as absolute(S) increases.
Therefore, KE has minimum value when S=0, and maximum when S=-0.5 and 0.5.
#5-e.
#5-e. Discussion: Implications for tropical cyclogenesis, in terms of convective heating profiles and their dependence on low-level rain evaporation and downdrafts.
T is calculated as below.h = h0*exp(-x/Lr)
PHI(=geopotential) = gh = gz
p = (rho)RT & p = (rho)gz --> RT=gz = gh
T = (g/R)*h
Therefore,T_mode1 = (g/R)* h0*exp(-x/Lr_m1)
T_mode2 = -S*(g/R)* h0*exp(-x/Lr_m2)
T = T_mode1*sin(m1z) + T_mode2*sin(m2z)
This is Temperature profile at S=0.5 (stratiform case).
As we can see, mode 1 and mode 2 has opposite sign of temperature in lower levels.
In lower levels, mode 2(=stratiform mode) causes cold temperature and downdraft by evaporating cooling as it rains,
while mode 1(=convective mode) still causes updraft.
Therefore, anticyclone by mode 2 and cyclone by mode 1 will be cancelled out, so cyclone will be weakened. This is unfavorable condition for cyclogenesis.
The opposite case is S=0.5 (shallow convection case) below.
In this case, mode 2(=shallow convection mode) will help to enhance cyclogenesis at lower levels.
+ about h0:
All calculations are performed without specified h0 in h=h0*exp(-x/Lr). (h0 is supposed to be 1 here.)Therefore, all values are not realistic. If h0 is given, they would get more realistic values.